A small ball problem and Chung’s law of iterated logarithm for a hypoelliptic Brownian motion in Heisenberg group are proven. In addition, bounds on the limit established.

In this paper, we study the Landau equation under Navier-Stokes scaling in torus for hard and moderately soft potentials. More precisely, investigate Cauchy theory a perturbative framework establish some new short time regularization estimates our rescaled nonlinear equation. These are quantified obtain instantaneous expected anisotropic gain of regularity (see [54] corresponding hypoelliptic o...

We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth hypoelliptic symbols. Methodological novelties and technical refinements appear embedded into classical strategies of proof in order to cope with most delicate...

We prove that if a super-Poincaré inequality is satisfied by an infinitesimal generator −A of a symmetric contraction semigroup on L2 and that is contracting on L1, then it implies a corresponding super-Poincaré inequality for −g(A) for any Bernstein function g. We also study the converse of this statement. We prove similar results for Nash-type inequalities. We apply our results to Euclidean, ...

Our purpose here is to announce results in harmonic analysis related to a large class of hypoelliptic operators on arbitrary simply-connected nilpotent Lie groups. We find the asymptotic development of their fundamental solutions, both locally and at infinity, and study corresponding Riesz transforms and analogues of the Hardy-Littlewood-Sobolev theorem for fractional integration. Details will ...

In this work, we prove the existence and uniqueness of a quasi-stationary distribution for hypoelliptic Hamiltonian dynamics system N particles in $${\mathbb {R}}^d$$ interacting with Lennard-Jones type potentials or repulsive Coulomb potentials.

The Hobson and Rogers model for option pricing is considered. This stochastic volatility model preserves the completeness of the market and can potentially reproduce the observed smile and term structure patterns of implied volatility. A calibration procedure based on ad-hoc numerical schemes for hypoelliptic PDEs is proposed and used to quantitatively investigate the pricing performance of the...

This article is concerned with maximal accretive realization of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible bou...